Endpoint control of multiple substrates of varying thickness on the same platen in chemical mechanical polishing

ABSTRACT

A difference between a first expected required polish time for a first substrate and a second expected required polish time for a second substrate is determined using a first pre-polish thickness and a second pre-polish thickness measured at an in-line metrology station. A duration of an initial period is determined based on the difference between the first expected required polish time and the second expected required polish time. For the initial period at a beginning of a polishing operation, no pressure is applied to whichever of the first substrate and the second substrate has a lesser expected required polish time while simultaneously pressure is applied to whichever of the first substrate and the second substrate has a greater expected required polish time. After the initial period, pressure is applied to both the first substrate and the second substrate.

TECHNICAL FIELD

The present disclosure relates generally to monitoring of multiplesubstrates during chemical mechanical polishing.

BACKGROUND

An integrated circuit is typically formed on a substrate by thesequential deposition of conductive, semiconductive, or insulativelayers on a silicon wafer. One fabrication step involves depositing afiller layer over a non-planar surface and planarizing the filler layer.For certain applications, the filler layer is planarized until the topsurface of a patterned layer is exposed. A conductive filler layer, forexample, can be deposited on a patterned insulative layer to fill thetrenches or holes in the insulative layer. After planarization, theportions of the conductive layer remaining between the raised pattern ofthe insulative layer form vias, plugs, and lines that provide conductivepaths between thin film circuits on the substrate. For otherapplications, such as oxide polishing, the filler layer is planarizeduntil a predetermined thickness is left over the non planar surface. Inaddition, planarization of the substrate surface is usually required forphotolithography.

Chemical mechanical polishing (CMP) is one accepted method ofplanarization. This planarization method typically requires that thesubstrate be mounted on a carrier head. The exposed surface of thesubstrate is typically placed against a rotating polishing pad with adurable roughened surface. The carrier head provides a controllable loadon the substrate to push it against the polishing pad. A polishingliquid, such as a slurry with abrasive particles, is typically suppliedto the surface of the polishing pad.

One problem in CMP is using an appropriate polishing rate to achieve adesirable profile, e.g., a substrate layer that has been planarized to adesired flatness or thickness, or a desired amount of material has beenremoved. Variations in the initial thickness of a substrate layer, theslurry composition, the polishing pad condition, the relative speedbetween the polishing pad and a substrate, and the load on a substratecan cause variations in the material removal rate across a substrate,and from substrate to substrate. These variations cause variations inthe time needed to reach the polishing endpoint and the amount removed.Therefore, it may not be possible to determine the polishing endpointmerely as a function of the polishing time, or to achieve a desiredprofile merely by applying a constant pressure.

In some systems, a substrate is optically monitored in-situ duringpolishing, e.g., through a window in the polishing pad. However,existing optical monitoring techniques may not satisfy increasingdemands of semiconductor device manufacturers.

SUMMARY

In one aspect, a computer-implemented method of polishing includesmeasuring a first pre-polish thickness of a layer of a first substrateat an in-line metrology station, measuring a second pre-polish thicknessof a layer of a second substrate at the in-line metrology station,simultaneously contacting the first substrate and the second substrateto the same polishing pad, wherein pressures applied to the firstsubstrate and the second substrate are independently controllable,determining a difference between a first expected required polish timefor the first substrate and a second expected required polish time forthe second substrate using the first pre-polish thickness and the secondpre-polish thickness, determining a duration of an initial period basedon the difference between the first expected required polish time andthe second expected required polish time, for the initial period at abeginning of a polishing operation, applying no pressure to whichever ofthe first substrate and the second substrate has a lesser expectedrequired polish time while simultaneously applying pressure to whicheverof the first substrate and the second substrate has a greater expectedrequired polish time, and after the initial period, applying pressure toboth the first substrate and the second substrate.

Implementations may include one or more of the following features. Afirst target thickness for the first substrate and a second targetthickness for the second substrate may be stored. The duration of theinitial period may be selected such that a thickness difference betweenthe first substrate and the second substrate is closer to a differencebetween the first target thickness and the second target thickness at anintermediate time before a projected endpoint time than without such aninitial period. The first target thickness may be equal to the secondtarget thickness. The first target thickness and the second targetthickness may be zero. The layer of the first substrate and the layer ofthe second substrate may be metal. The first target thickness may besubtracted from the first pre-polish thickness to determine a firstamount to remove from the first substrate and the second targetthickness may be subtracted from the second pre-polish thickness todetermine a second amount to remove from the second substrate.Determining the difference between the first expected required polishtime and the second expected required polish time may include storing apolishing rate calculated prior to polishing of the first substrate andthe second substrate. Determining the difference between the firstexpected required polish time and the second expected required polishtime may include dividing the first amount to remove by the polishingrate to determine the first expected required polish time, and dividingthe second amount to remove by the polishing rate to determine thesecond expected required polish time. The polishing rate may becalculated by determining the polishing rate of at least one substratepolished on the polishing pad before polishing of the first substrateand the second substrate. Determining the polishing rate may includecalculating a moving average of polishing rates of a plurality ofsubstrates polished on the polishing pad before polishing of the firstsubstrate and the second substrate. The initial period may equal thedifference between the first expected required polish time and thesecond expected required polish time. The first substrate and the secondsubstrate may be monitored during polishing with an in-situ monitoringsystem. At a time after the initial period, the pressure of at least oneof the first or second substrate may be adjusted such that the firstsubstrate and the second substrate reach target thickness at closer tothe same time than without such adjustment.

In another aspect, a computer-implemented method of polishing includesmeasuring a first pre-polish thickness of a layer of a first substrateat an in-line metrology station, measuring a second pre-polish thicknessof a layer of a second substrate at the in-line metrology station,simultaneously contacting the first substrate and the second substrateto the same polishing pad, wherein pressures applied to the firstsubstrate and the second substrate are independently controllable,determining a difference between a first expected required polish timefor the first substrate and a second expected required polish time forthe second substrate based on the first pre-polish thickness and thesecond pre-polish thickness, determining a pressure ratio to applybetween the first substrate and the second substrate using thedifference between the first expected required polish time and thesecond expected required polish time such that the first substrate andthe second substrate have closer to the same thickness at anintermediate time before a projected endpoint time than without such apressure difference, and at least until the intermediate time, applyingpressures to the first substrate and the second substrate at thepressure ratio.

Implementations may include one or more of the following features. Thepressure ratio may equal the ratio between the second expected requiredpolish time and the first expected required polish time. A first targetthickness for the first substrate and a second target thickness for thesecond substrate may be stored. Polishing of the first substrate and thesecond substrate may be commenced at a substantially same time. Thefirst target thickness may be equal to the second target thickness. Thefirst target thickness and the second target thickness may be zero. Thelayer of the first substrate and the layer of the second substrate maybe metal. The first target thickness may be subtracted from the firstpre-polish thickness to determine a first amount to remove from thefirst substrate and the second target thickness may be subtracted fromthe second pre-polish thickness to determine a second amount to removefrom the second substrate. The difference between the first expectedrequired polish time and the expected required second polish time may bedetermined based on a polishing rate calculated prior to polishing ofthe first substrate and the second substrate. Determining the differencebetween the first expected required polish time and the second expectedrequired polish time may include dividing the first amount to remove bythe polishing rate to determine the first expected required polishingtime, and dividing the second amount to remove by the polishing rate todetermine the second expected required polishing time. The polishingrate may be calculated by determining the polishing rate of at least onesubstrate polished on the polishing pad before polishing of the firstsubstrate and the second substrate. Determining the polishing rate mayinclude calculating a moving average of polishing rates of a pluralityof substrates polished on the polishing pad before polishing of thefirst substrate and the second substrate. The first substrate and thesecond substrate may be monitored during polishing with an in-situmonitoring system. At a time after the initial period, the pressure ofat least one of the first or second substrate may be adjusted such thatthe first substrate and the second substrate reach target thickness atcloser to the same time than without such adjustment.

In other aspects, polishing systems and computer-program productstangibly embodied on a computer readable medium are provided to carryout these methods.

Certain implementations may have one or more of the followingadvantages. If all of the substrates on the same platen endpoint atapproximately the same time, defects can be avoided, such as scratchescaused by rinsing a substrate with water too early or corrosion causedby failing to rinse a substrate in a timely manner. Equalizing polishingtimes across multiple substrates can also improve throughput. Substrateswith different incoming layer thicknesses can be polished to the sametarget thickness more reliably. Equalizing polishing times for differentzones within a substrate can also decrease within-wafer non-uniformity(WIWNU), i.e., improve substrate layer uniformity. In addition, it maybe possible to provide a substrate with a deliberately pre-selectednon-uniformity, e.g., variance of a substrate from a target profile canbe decreased.

The details of one or more embodiments are set forth in the accompanyingdrawings and the description below. Other features, aspects, andadvantages will become apparent from the description, the drawings, andthe claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic cross-sectional view of an example of apolishing apparatus having two polishing heads.

FIG. 2 illustrates a schematic top view of a substrate having multiplezones.

FIG. 3A illustrates a top view of a polishing pad and shows locationswhere in-situ measurements are taken on a first substrate.

FIG. 3B illustrates a top view of a polishing pad and shows locationswhere in-situ measurements are taken on a second substrate.

FIG. 4 illustrates a measured spectrum from the in-situ opticalmonitoring system.

FIG. 5 illustrates a library of reference spectra.

FIG. 6 illustrates an index trace.

FIG. 7 illustrates a plurality of index traces for different zones ofdifferent substrates.

FIG. 8 illustrates a calculation of a plurality of desired slopes for aplurality of adjustable zones based on a time that an index trace of areference zone reaches a target index.

FIG. 9 illustrates a calculation of a plurality of desired slopes for aplurality of adjustable zones based on a time that an index trace of areference zone reaches a target index.

FIG. 10 illustrates a plurality of index traces for different zones ofdifferent substrates, with different zones having different targetindexes.

FIG. 11 illustrates a calculation of an endpoint for different zonesbased on a time that an index trace of a reference zone reaches a targetindex.

FIG. 12 illustrates a calculation of time offset between polishstart-times of two substrates of differing thickness.

FIG. 13 illustrates a calculation of time offset between polishstart-times of two substrates of differing thickness.

FIG. 14 is a flow diagram of an example process for adjusting thepolishing rate of a plurality of zones in a plurality of substrates suchthat the plurality of zones have approximately the same thickness at thetarget time.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

Where multiple substrates are being polished simultaneously, e.g., onthe same polishing pad, polishing rate variations between the substratescan lead to the substrates reaching their target thickness at differenttimes. On the one hand, if polishing is halted simultaneously for thesubstrates, then some will not be at the desired thickness. On the otherhand, if polishing for the substrates is stopped at different times,then some substrates may have defects and the polishing apparatus isoperating at lower throughput.

In some cases, the initial thicknesses of two substrates on a sameplaten can be different. In such cases, starting the polishing operationon both substrates simultaneously with substantially same polishingrates may lead to the thinner substrate reaching the polishing end pointsooner than the thicker substrate. However, since it is desirable torinse the substrates simultaneously and as soon as the polishing endpoints are reached, it could be of interest to adjust the polishingprocess such that the end points for both substrates are reachedtogether or at least within short time from each other. By determining atime offset for starting the polishing operations of the two substratesthe substrates can be made to achieve closer endpoint conditions. By“closer endpoint conditions,” it is meant that the substrates wouldreach their target thickness closer to the same time than without thetime offset, or if the substrates halt polishing at the same time, thatthe substrates would have closer to the same thickness than without thetime offset.

FIG. 1 illustrates an example of a polishing apparatus 100. Thepolishing apparatus 100 includes a rotatable disk-shaped platen 120 onwhich a polishing pad 110 is situated. The platen is operable to rotateabout an axis 125. For example, a motor 121 can turn a drive shaft 124to rotate the platen 120. The polishing pad 110 can be detachablysecured to the platen 120, for example, by a layer of adhesive. Thepolishing pad 110 can be a two-layer polishing pad with an outerpolishing layer 112 and a softer backing layer 114.

The polishing apparatus 100 can include a combined slurry/rinse arm 130.During polishing, the arm 130 is operable to dispense a polishing liquid132, such as a slurry, onto the polishing pad 110. While only oneslurry/rinse arm 130 is shown, additional nozzles, such as one or morededicated slurry arms per carrier head, can be used. The polishingapparatus can also include a polishing pad conditioner to abrade thepolishing pad 110 to maintain the polishing pad 110 in a consistentabrasive state.

In this embodiment, the polishing apparatus 100 includes two (or two ormore) carrier heads 140. Each carrier head 140 is operable to hold asubstrate 10 (e.g., a first substrate 10 a at one carrier head and asecond substrate 10 b at the other carrier head) against the polishingpad 110. Each carrier head 140 can have independent control of thepolishing parameters, for example pressure, associated with eachrespective substrate.

In particular, each carrier head 140 can include a retaining ring 142 toretain the substrate 10 below a flexible membrane 144. Each carrier head140 also includes a plurality of independently controllablepressurizable chambers defined by the membrane, e.g., 3 chambers 146a-146 c, which can apply independently controllable pressurizes toassociated zones 148 a-148 c on the flexible membrane 144 and thus onthe substrate 10 (see FIG. 2). Referring to FIG. 2, the center zone 148a can be substantially circular, and the remaining zones 148 b-148 e canbe concentric annular zones around the center zone 148 a. Although onlythree chambers are illustrated in FIGS. 1 and 2 for ease ofillustration, there could be two chambers, or four or more chambers,e.g., five chambers.

Returning to FIG. 1, each carrier head 140 is suspended from a supportstructure 150, e.g., a carousel, and is connected by a drive shaft 152to a carrier head rotation motor 154 so that the carrier head can rotateabout an axis 155. Optionally each carrier head 140 can oscillatelaterally, e.g., on sliders on the carousel 150; or by rotationaloscillation of the carousel itself. In operation, the platen is rotatedabout its central axis 125, and each carrier head is rotated about itscentral axis 155 and translated laterally across the top surface of thepolishing pad.

While only two carrier heads 140 are shown, more carrier heads can beprovided to hold additional substrates so that the surface area ofpolishing pad 110 may be used efficiently. Thus, the number of carrierhead assemblies adapted to hold substrates for a simultaneous polishingprocess can be based, at least in part, on the surface area of thepolishing pad 110.

The polishing apparatus also includes an in-situ monitoring system 160,which can be used to determine whether to adjust a polishing rate or anadjustment for the polishing rate as discussed below. The in-situmonitoring system 160 can include an optical monitoring system, e.g., aspectrographic monitoring system, or an eddy current monitoring system.

In one embodiment, the monitoring system 160 is an optical monitoringsystem. An optical access through the polishing pad is provided byincluding an aperture (i.e., a hole that runs through the pad) or asolid window 118. The solid window 118 can be secured to the polishingpad 110, e.g., as a plug that fills an aperture in the polishing pad,e.g., is molded to or adhesively secured to the polishing pad, althoughin some implementations the solid window can be supported on the platen120 and project into an aperture in the polishing pad.

The optical monitoring system 160 can include a light source 162, alight detector 164, and circuitry 166 for sending and receiving signalsbetween a remote controller 190, e.g., a computer, and the light source162 and light detector 164. One or more optical fibers can be used totransmit the light from the light source 162 to the optical access inthe polishing pad, and to transmit light reflected from the substrate 10to the detector 164. For example, a bifurcated optical fiber 170 can beused to transmit the light from the light source 162 to the substrate 10and back to the detector 164. The bifurcated optical fiber an include atrunk 172 positioned in proximity to the optical access, and twobranches 174 and 176 connected to the light source 162 and detector 164,respectively.

In some implementations, the top surface of the platen can include arecess 128 into which is fit an optical head 168 that holds one end ofthe trunk 172 of the bifurcated fiber. The optical head 168 can includea mechanism to adjust the vertical distance between the top of the trunk172 and the solid window 118.

The output of the circuitry 166 can be a digital electronic signal thatpasses through a rotary coupler 129, e.g., a slip ring, in the driveshaft 124 to the controller 190 for the optical monitoring system.Similarly, the light source can be turned on or off in response tocontrol commands in digital electronic signals that pass from thecontroller 190 through the rotary coupler 129 to the optical monitoringsystem 160. Alternatively, the circuitry 166 could communicate with thecontroller 190 by a wireless signal.

The light source 162 can be operable to emit white light. In oneimplementation, the white light emitted includes light havingwavelengths of 200-800 nanometers. A suitable light source is a xenonlamp or a xenon mercury lamp.

The light detector 164 can be a spectrometer. A spectrometer is anoptical instrument for measuring intensity of light over a portion ofthe electromagnetic spectrum. A suitable spectrometer is a gratingspectrometer. Typical output for a spectrometer is the intensity of thelight as a function of wavelength (or frequency).

As noted above, the light source 162 and light detector 164 can beconnected to a computing device, e.g., the controller 190, operable tocontrol their operation and receive their signals. The computing devicecan include a microprocessor situated near the polishing apparatus,e.g., a programmable computer. With respect to control, the computingdevice can, for example, synchronize activation of the light source withthe rotation of the platen 120.

In some implementations, the light source 162 and detector 164 of thein-situ monitoring system 160 are installed in and rotate with theplaten 120. In this case, the motion of the platen will cause the sensorto scan across each substrate. In particular, as the platen 120 rotates,the controller 190 can cause the light source 162 to emit a series offlashes starting just before and ending just after each substrate 10passes over the optical access. Alternatively, the computing device cancause the light source 162 to emit light continuously starting justbefore and ending just after each substrate 10 passes over the opticalaccess. In either case, the signal from the detector can be integratedover a sampling period to generate spectra measurements at a samplingfrequency.

In operation, the controller 190 can receive, for example, a signal thatcarries information describing a spectrum of the light received by thelight detector for a particular flash of the light source or time frameof the detector. Thus, this spectrum is a spectrum measured in-situduring polishing.

As shown by in FIG. 3A, if the detector is installed in the platen, dueto the rotation of the platen (shown by arrow 204), as the window 108travels below one carrier head (e.g., the carrier head holding the firstsubstrate 10 a), the optical monitoring system making spectrameasurements at a sampling frequency will cause the spectra measurementsto be taken at locations 201 in an arc that traverses the firstsubstrate 10 a. For example, each of points 201 a-201 k represents alocation of a spectrum measurement by the monitoring system of the firstsubstrate 10 a (the number of points is illustrative; more or fewermeasurements can be taken than illustrated, depending on the samplingfrequency). As shown, over one rotation of the platen, spectra areobtained from different radii on the substrate 10 a. That is, somespectra are obtained from locations closer to the center of thesubstrate 10 a and some are closer to the edge. Similarly, as shown byin FIG. 3B, due to the rotation of the platen, as the window travelsbelow the other carrier head (e.g., the carrier head holding the secondsubstrate 10 b) the optical monitoring system making spectrameasurements at the sampling frequency will cause the spectrameasurements to be taken at locations 202 along an arc that traversesthe second substrate 10 b.

Thus, for any given rotation of the platen, based on timing and motorencoder information, the controller can determine which substrate, e.g.,substrate 10 a or 10 b, is the source of the measured spectrum. Inaddition, for any given scan of the optical monitoring system across asubstrate, e.g., substrate 10 a or 10 b, based on timing, motor encoderinformation, and optical detection of the edge of the substrate and/orretaining ring, the controller 190 can calculate the radial position(relative to the center of the particular substrate 10 a or 10 b beingscanned) for each measured spectrum from the scan. The polishing systemcan also include a rotary position sensor, e.g., a flange attached to anedge of the platen that will pass through a stationary opticalinterrupter, to provide additional data for determination of whichsubstrate and the position on the substrate of the measured spectrum.The controller can thus associate the various measured spectra with thecontrollable zones 148 b-148 e (see FIG. 2) on the substrates 10 a and10 b. In some implementations, the time of measurement of the spectrumcan be used as a substitute for the exact calculation of the radialposition.

Over multiple rotations of the platen, for each zone of each substrate,a sequence of spectra can be obtained over time. Without being limitedto any particular theory, the spectrum of light reflected from thesubstrate 10 evolves as polishing progresses (e.g., over multiplerotations of the platen, not during a single sweep across the substrate)due to changes in the thickness of the outermost layer, thus yielding asequence of time-varying spectra. Moreover, particular spectra areexhibited by particular thicknesses of the layer stack.

In some implementations, the controller, e.g., the computing device, canbe programmed to compare a measured spectrum to multiple referencespectra to and determine which reference spectrum provides the bestmatch. In particular, the controller can be programmed to compare eachspectrum from a sequence of measured spectra from each zone of eachsubstrate to multiple reference spectra to generate a sequence of bestmatching reference spectra for each zone of each substrate.

As used herein, a reference spectrum is a predefined spectrum generatedprior to polishing of the substrate. A reference spectrum can have apre-defined association, i.e., defined prior to the polishing operation,with a value representing a time in the polishing process at which thespectrum is expected to appear, assuming that the actual polishing ratefollows an expected polishing rate. Alternatively or in addition, thereference spectrum can have a pre-defined association with a value of asubstrate property, such as a thickness of the outermost layer.

A reference spectrum can be generated empirically, e.g., by measuringthe spectra from a test substrate, e.g., a test substrate having a knowninitial layer thicknesses. For example, to generate a plurality ofreference spectra, a set-up substrate is polished using the samepolishing parameters that would be used during polishing of devicewafers while a sequence of spectra are collected. For each spectrum, avalue is recorded representing the time in the polishing process atwhich the spectrum was collected. For example, the value can be anelapsed time, or a number of platen rotations. The substrate can beoverpolished, i.e., polished past a desired thickness, so that thespectrum of the light that reflected from the substrate when the targetthickness is achieved can be obtained.

In order to associate each spectrum with a value of a substrateproperty, e.g., a thickness of the outermost layer, the initial spectraand property of a “set-up” substrate with the same pattern as theproduct substrate can be measured pre-polish at a metrology station. Thefinal spectrum and property can also be measured post-polish with thesame metrology station or a different metrology station. The propertiesfor spectra between the initial spectra and final spectra can bedetermined by interpolation, e.g., linear interpolation based on elapsedtime at which the spectra of the test substrate was measured.

In addition to being determined empirically, some or all of thereference spectra can be calculated from theory, e.g., using an opticalmodel of the substrate layers. For example, and optical model can beused to calculate a reference spectrum for a given outer layer thicknessD. A value representing the time in the polishing process at which thereference spectrum would be collected can be calculated, e.g., byassuming that the outer layer is removed at a uniform polishing rate.For example, the time Ts for a particular reference spectrum can becalculated simply by assuming a starting thickness D0 and uniformpolishing rate R (Ts=(D0−D)/R). As another example, linear interpolationbetween measurement times T1, T2 for the pre-polish and post-polishthicknesses D1, D2 (or other thicknesses measured at the metrologystation) based on the thickness D used for the optical model can beperformed (Ts=T2−T1*(D1−D)/(D1−D2)).

Referring to FIGS. 4 and 5, a measured spectrum 300 (see FIG. 4) can becompared to reference spectra 320 from one or more libraries 310 (seeFIG. 5). As used herein, a library of reference spectra is a collectionof reference spectra which represent substrates that share a property incommon. However, the property shared in common in a single library mayvary across multiple libraries of reference spectra. For example, twodifferent libraries can include reference spectra that representsubstrates with two different underlying thicknesses. For a givenlibrary of reference spectra, variations in the upper layer thickness,rather than other factors (such as differences in wafer pattern,underlying layer thickness, or layer composition), can be primarilyresponsible for the differences in the spectral intensities.

Reference spectra 320 for different libraries 310 can be generated bypolishing multiple “set-up” substrates with different substrateproperties (e.g., underlying layer thicknesses, or layer composition)and collecting spectra as discussed above; the spectra from one set-upsubstrate can provide a first library and the spectra from anothersubstrate with a different underlying layer thickness can provide asecond library. Alternatively or in addition, reference spectra fordifferent libraries can be calculated from theory, e.g., spectra for afirst library can be calculated using the optical model with theunderlying layer having a first thickness, and spectra for a secondlibrary can be calculated using the optical model with the underlyinglayer having a different thickness.

In some implementations, each reference spectrum 320 is assigned anindex value 330. In general, each library 310 can include many referencespectra 320, e.g., one or more, e.g., exactly one, reference spectra foreach platen rotation over the expected polishing time of the substrate.This index 330 can be the value, e.g., a number, representing the timein the polishing process at which the reference spectrum 320 is expectedto be observed. The spectra can be indexed so that each spectrum in aparticular library has a unique index value. The indexing can beimplemented so that the index values are sequenced in an order in whichthe spectra were measured. An index value can be selected to changemonotonically, e.g., increase or decrease, as polishing progresses. Inparticular, the index values of the reference spectra can be selected sothat they form a linear function of time or number of platen rotations(assuming that the polishing rate follows that of the model or testsubstrate used to generate the reference spectra in the library). Forexample, the index value can be proportional, e.g., equal, to a numberof platen rotations at which the reference spectra was measured for thetest substrate or would appear in the optical model. Thus, each indexvalue can be a whole number. The index number can represent the expectedplaten rotation at which the associated spectrum would appear.

The reference spectra and their associated index values can be stored ina reference library. For example, each reference spectrum 320 and itsassociated index value 330 can be stored in a record 340 of database350. The database 350 of reference libraries of reference spectra can beimplemented in memory of the computing device of the polishingapparatus.

As noted above, for each zone of each substrate, based on the sequenceof measured spectra or that zone and substrate, the controller 190 canbe programmed to generate a sequence of best matching spectra. A bestmatching reference spectrum can be determined by comparing a measuredspectrum to the reference spectra from a particular library.

In some implementations, the best matching reference spectrum can bedetermined by calculating, for each reference spectra, a sum of squareddifferences between the measured spectrum and the reference spectrum.The reference spectrum with the lowest sum of squared differences hasthe best fit. Other techniques for finding a best matching referencespectrum are possible, e.g., performing a cross-correlation between themeasured spectrum and each reference spectrum, and selecting thereference spectrum with the greatest correlation as the best matchingreference spectrum.

A method that can be applied to decrease computer processing is to limitthe portion of the library that is searched for matching spectra. Thelibrary typically includes a wider range of spectra than will beobtained while polishing a substrate. During substrate polishing, thelibrary searching is limited to a predetermined range of libraryspectra. In some embodiments, the current rotational index N of asubstrate being polished is determined. For example, in an initialplaten rotation, N can be determined by searching all of the referencespectra of the library. For the spectra obtained during a subsequentrotation, the library is searched within a range of freedom of N. Thatis, if during one rotation the index number is found to be N, during asubsequent rotation which is X rotations later, where the freedom is Y,the range that will be searched from (N+X)−Y to (N+X)+Y.

Referring to FIG. 6, which illustrates the results for only a singlezone of a single substrate, the index value of each of the best matchingspectra in the sequence can be determined to generate a time-varyingsequence of index values 212. This sequence of index values can betermed an index trace 210. In some implementations, an index trace isgenerated by comparing each measured spectrum to the reference spectrafrom exactly one library. In general, the index trace 210 can includeone, e.g., exactly one, index value per sweep of the optical monitoringsystem below the substrate.

For a given index trace 210, where there are multiple spectra measuredfor a particular substrate and zone in a single sweep of the opticalmonitoring system (termed “current spectra”), a best match can bedetermined between each of the current spectra and the reference spectraof one or more, e.g., exactly one, library. In some implementations,each selected current spectra is compared against each reference spectraof the selected library or libraries. Given current spectra e, f, and g,and reference spectra E, F, and G, for example, a matching coefficientcould be calculated for each of the following combinations of currentand reference spectra: e and E, e and F, e and G, f and E, f and F, fand G, g and E, g and F, and g and G. Whichever matching coefficientindicates the best match, e.g., is the smallest, determines thebest-matching reference spectrum, and thus the index value.Alternatively, in some implementations, the current spectra can becombined, e.g., averaged, and the resulting combined spectrum iscompared against the reference spectra to determine the best match, andthus the index value.

In some implementations, for at least some zones of some substrates, aplurality of index traces can be generated. For a given zone of a givensubstrate, an index trace can be generated for each reference library ofinterest. That is, for each reference library of interest to the givenzone of the given substrate, each measured spectrum in a sequence ofmeasured spectra is compared to reference spectra from a given library,a sequence of the best matching reference spectra is determined, and theindex values of the sequence of best matching reference spectra providethe index trace for the given library.

In summary, each index trace includes a sequence 210 of index values212, with each particular index value 212 of the sequence beinggenerated by selecting the index of the reference spectrum from a givenlibrary that is the closest fit to the measured spectrum. The time valuefor each index of the index trace 210 can be the same as the time atwhich the measured spectrum was measured.

Referring to FIG. 7, a plurality of index traces is illustrated. Asdiscussed above, an index trace can be generated for each zone of eachsubstrate. For example, a first sequence 210 of index values 212 (shownby hollow circles) can be generated for a first zone of a firstsubstrate, a second sequence 220 of index values 222 (shown by solidcircles) can be generated for a second zone of the first substrate, athird sequence 230 of index values 232 (shown by hollow squares) can begenerated for a first zone of a second substrate, and a fourth sequence240 of index values 242 (shown by solid squares) can be generated for asecond zone of the second substrate.

As shown in FIG. 7, for each substrate index trace, a polynomialfunction of known order, e.g., a first-order function (e.g., a line) isfit to the sequence of index values for the associated zone and wafer,e.g., using robust line fitting. For example, a first line 214 can befit to index values 212 for the first zone of the first substrate, asecond line 224 can be fit to the index values 222 of the second zone ofthe first substrate, a third line 234 can be fit to the index values 232of the first zone of the second substrate, and a fourth line 244 can befit to the index values 242 of the second zone of the second substrate.Fitting of a line to the index values can include calculation of theslope S of the line and an x-axis intersection time T at which the linecrosses a starting index value, e.g., 0. The function can be expressedin the form I(t)=S·(t−T), where t is time. The x-axis intersection timeT can have a negative value, indicating that the starting thickness ofthe substrate layer is less than expected. Thus, the first line 214 canhave a first slope S1 and a first x-axis intersection time T1, thesecond line 224 can have a second slope S2 and a second x-axisintersection time T2, the third line 234 can have a third slope S3 and athird x-axis intersection time T3, and the fourth line 244 can have afourth slope S4 and a fourth x-axis intersection time T4.

At some during the polishing process, e.g., at a time T0, a polishingparameter for at least one zone of at least one substrate, e.g., atleast one zone of every substrate, is adjusted to adjust the polishingrate of the zone of the substrate such that at a polishing endpointtime, the plurality of zones of the plurality of substrates are closerto their target thickness than without such adjustment. In someembodiments, each zone of the plurality of substrates can haveapproximately the same thickness at the endpoint time.

Referring to FIG. 8, in some implementations, one zone of one substrateis selected as a reference zone, and a projected endpoint time TE atwhich the reference zone will reach a target index IT is determined. Forexample, as shown in FIG. 8, the first zone of the first substrate isselected as the reference zone, although a different zone and/or adifferent substrate could be selected. The target thickness IT is set bythe user prior to the polishing operation and stored.

In order to determine the projected time at which the reference zonewill reach the target index, the intersection of the line of thereference zone, e.g., line 214, with the target index, IT, can becalculated. Assuming that the polishing rate does not deviate from theexpected polishing rate through the remainder polishing process, thenthe sequence of index values should retain a substantially linearprogression. Thus, the expected endpoint time TE can be calculated as asimple linear interpolation of the line to the target index IT, e.g.,IT=S·(TE−T). Thus, in the example of FIG. 8 in which the first zone ofthe second substrate is selected as the reference zone, with associatedthird line 234, IT=S1·(TE−T1), i.e., TE=IT/S1−T1.

One or more zones, e.g., all zones, other than the reference zone(including zones on other substrates) can be defined as adjustablezones. Where the lines for the adjustable zones meet the expectedendpoint time TE define projected endpoint for the adjustable zones. Thelinear function of each adjustable zone, e.g., lines 224, 234 and 244 inFIG. 8, can thus be used to extrapolate the index, e.g., EI2, EI3 andEI4, that will be achieved at the expected endpoint time ET for theassociated zone. For example, the second line 224 can be used toextrapolate the expected index, EI2, at the expected endpoint time ETfor the second zone of the first substrate, the third line 234 can beused to extrapolate the expected index, EI3, at the expected endpointtime ET for the first zone of the second substrate, and the fourth linecan be used to extrapolate the expected index, EI4, at the expectedendpoint time ET for the second zone of the second substrate.

As shown in FIG. 8, if no adjustments are made to the polishing rate ofany of the zones of any the substrates after time T0, then if endpointis forced at the same time for all substrates, then each substrate canhave a different thickness, or each substrate could have a differentendpoint time (which is not desirable because it can lead to defects andloss of throughput). Here, for example, the second zone of the firstsubstrate (shown by line 224) would endpoint at an expected index EI2lower (and thus a thickness less) than the expected index of the firstzone of the first substrate. Likewise, the first zone of the secondsubstrate (shown by line 234) would endpoint at an expected index EI3less (and thus a thickness less) than the first zone of the firstsubstrate. The second zone of the second substrate (shown by line 244)would endpoint at an expected index EI4 greater (and thus a thicknessgreater) than the first zone of the first substrate.

If, as shown in FIG. 8, the target index will be reached at differenttimes for different substrates (or equivalently, the adjustable zoneswill have different expected indexes at the projected endpoint time ofreference zone), the polishing rate can be adjusted upwardly ordownwardly, such that the substrates would reach the target index (andthus target thickness) closer to the same time than without suchadjustment, e.g., at approximately the same time, or would have closerto the same index value (and thus same thickness), at the target timethan without such adjustment, e.g., approximately the same index value(and thus approximately the same thickness).

Thus, in the example of FIG. 8, commencing at a time T0, at least onepolishing parameter for the second zone of the first substrate ismodified so that the polishing rate of the zone is decreased (and as aresult the slope of the index trace 220 is decreased). Also, in thisexample, at least one polishing parameter for the second zone of thesecond substrate is modified so that the polishing rate of the zone isdecreased (and as a result the slope of the index trace 240 isdecreased). Similarly, in this example, at least one polishing parameterfor the first zone of the second substrate is modified so that thepolishing rate of the zone is increased (and as a result the slope ofthe index trace 240 is increased). As a result both zones of bothsubstrates would reach the target index (and thus the target thickness)at approximately the same time (or if polishing of both substrates haltsat the same time, both zones of both substrates will end withapproximately the same thickness).

In some implementations, if the projected index at the expected endpointtime ET indicate that a zone of the substrate is within a predefinedrange of the target thickness, then no adjustment may be required forthat zone. The range may be 2%, e.g., within 1%, of the target index.

The polishing rates for the adjustable zones can be adjusted so that allof the zones are closer to the target index at the expected endpointtime than without such adjustment. For example, a reference zone of thereference substrate might be chosen and the processing parameters forall of the other zone adjusted such that all of the zones will endpointat approximately the projected time of the reference substrate. Thereference zone can be, for example, a predetermined zone, e.g., thecenter zone 148 a or the zone 148 b immediately surrounding the centerzone, the zone having the earliest or latest projected endpoint time ofany of the zones of any of the substrates, or the zone of a substratehaving the desired projected endpoint. The earliest time is equivalentto the thinnest substrate if polishing is halted at the same time.Likewise, the latest time is equivalent to the thickest substrate ifpolishing is halted at the same time. The reference substrate can be,for example, a predetermined substrate, a substrate having the zone withthe earliest or latest projected endpoint time of the substrates. Theearliest time is equivalent to the thinnest zone if polishing is haltedat the same time. Likewise, the latest time is equivalent to thethickest zone if polishing is halted at the same time.

For each of the adjustable zones, a desired slope for the index tracecan be calculated such that the adjustable zone reaches the target indexat the same time as the reference zone. For example, the desired slopeSD can be calculated from (IT−I)=SD*(TE−T0), where I is the index value(calculated from the linear function fit to the sequence of indexvalues) at time T0 polishing parameter is to be changed, IT is thetarget index, and TE is the calculated expected endpoint time. In theexample of FIG. 8, for the second zone of the first substrate, thedesired slope SD2 can be calculated from (IT−I2)=SD2*(TE−T0), for thefirst zone of the second substrate, the desired slope SD3 can becalculated from (IT−I3)=SD3*(TE−T0), and for the second zone of thesecond substrate, the desired slope SD4 can be calculated from(IT−I4)=SD4*(TE−T0).

Referring to FIG. 9, in some implementations, there is no referencezone. For example, the expected endpoint time TE′ can be a predeterminedtime, e.g., set by the user prior to the polishing process, or can becalculated from an average or other combination of the expected endpointtimes of two or more zones (as calculated by projecting the lines forvarious zones to the target index) from one or more substrates. In thisimplementation, the desired slopes are calculated substantially asdiscussed above (using the expected endpoint time TE′ rather than TE),although the desired slope for the first zone of the first substratemust also be calculated, e.g., the desired slope SD1 can be calculatedfrom (IT−I1)=SD1*(TE′−T0).

Referring to FIG. 10, in some implementations, (which can also becombined with the implementation shown in FIG. 9), there are differenttarget indexes for different zones. This permits the creation of adeliberate but controllable non-uniform thickness profile on thesubstrate. The target indexes can be entered by user, e.g., using aninput device on the controller. For example, the first zone of the firstsubstrate can have a first target indexes IT1, the second zone of thefirst substrate can have a second target indexes IT2, the first zone ofthe second substrate can have a third target indexes IT3, and the secondzone of the second substrate can have a fourth target indexes IT4.

The desired slope SD for each adjustable zone can be calculated from(IT−I)=SD*(TE−T0), where I is the index value of the zone (calculatedfrom the linear function fit to the sequence of index values for thezone) at time T0 at which the polishing parameter is to be changed, ITis the target index of the particular zone, and TE is the calculatedexpected endpoint time (either from a reference zone as discussed abovein relation to FIG. 8, or from a preset endpoint time or from acombination of expected endpoint times as discussed above in relation toFIG. 9). In the example of FIG. 10, for the second zone of the firstsubstrate, the desired slope SD2 can be calculated from(IT2−I2)=SD2*(TE−T0), for the first zone of the second substrate, thedesired slope SD3 can be calculated from (IT3−I3)=SD3*(TE−T0), and forthe second zone of the second substrate, the desired slope SD4 can becalculated from (IT4−I4)=SD4*(TE−T0).

For any of the above methods described above for FIGS. 8-10, thepolishing rate is adjusted to bring the slope of index trace closer tothe desired slope. The polishing rates can be adjusted by, for example,increasing or decreasing the pressure in a corresponding chamber of acarrier head. The change in polishing rate can be assumed to be directlyproportional to the change in pressure, e.g., a simple Prestonian model.For example, for each zone of each substrate, where zone was polishedwith a pressure P_(old) prior to the time T0, a new pressure P_(new) toapply after time T0 can be calculated as P_(new)=P_(old)*(SD/S), where Sis the slope of the line prior to time T0 and SD is the desired slope.

For example, assuming that pressure P_(old1) was applied to the firstzone of the first substrate, pressure P_(old2) was applied to the secondzone of the first substrate, pressure Pold3 was applied to the firstzone of the second substrate, and pressure Pold4 was applied to thesecond zone of the second substrate, then new pressure Pnew1 for thefirst zone of the first substrate can be calculated asP_(new1)=P_(old1)*(SD1/S1), the new pressure Pnew2 for the second zoneof the first substrate clan be calculated as P_(new2)=P_(old2)*(SD2/S2),the new pressure Pnew3 for the first zone of the second substrate clanbe calculated as P_(new3)=P_(old3)*(SD3/S3), and the new pressure Pnew4for the second zone of the second substrate clan be calculated asP_(new4)=P_(old4)*(SD4/S4).

The process of determining projected times that the substrates willreach the target thickness, and adjusting the polishing rates, can beperformed just once during the polishing process, e.g., at a specifiedtime, e.g., 40 to 60% through the expected polishing time, or performedmultiple times during the polishing process, e.g., every thirty to sixtyseconds. At a subsequent time during the polishing process, the ratescan again be adjusted, if appropriate. During the polishing process,changes in the polishing rates can be made only a few times, such asfour, three, two or only one time. The adjustment can be made near thebeginning, at the middle or toward the end of the polishing process.

Polishing continues after the polishing rates have been adjusted, e.g.,after time T0, the optical monitoring system continues to collectspectra for at least the reference zone and determine index values forthe reference zone. In some implementations, the optical monitoringsystem continues to collect spectra and determine index values for eachzone of each substrate. Once the index trace of a reference zone reachesthe target index, endpoint is called and the polishing operation stopsfor both substrates.

For example, as shown in FIG. 11, after time T0, the optical monitoringsystem continues to collect spectra for the reference zone and determineindex values 312 for the reference zone. If the pressure on thereference zone did not change (e.g., as in the implementation of FIG.8), then the linear function can be calculated using data points fromboth before T0 and after T0 to provide an updated linear function 314,and the time at which the linear function 314 reaches the target indexIT indicates the polishing endpoint time. On the other hand, if thepressure on the reference zone changed at time T0 (e.g., as in theimplementation of FIG. 9), then a new linear function 314 with a slopeS′ can be calculated from the sequence of index values 312 after timeT0, and the time at which the new linear function 314 reaches the targetindex IT indicates the polishing endpoint time. The reference zone usedfor determining endpoint can be the same reference zone used asdescribed above to calculate the expected endpoint time, or a differentzone (or if all of the zones were adjusted as described with referenceto FIG. 8, then a reference zone can be selected for the purpose ofendpoint determination). If the new linear function 314 reaches thetarget index IT slightly later (as shown in FIG. 11) or earlier than theprojected time calculated from the original linear function 214, thenone or more of the zones may be slightly overpolished or underpolished,respectively. However, since the difference between the expectedendpoint time and the actual polishing time should be less a coupleseconds, this need not severely impact the polishing uniformity.

In some implementations, e.g., for copper polishing, after detection ofthe endpoint for a substrate, the substrate is immediately subjected toan overpolishing process, e.g., to remove copper residue. Theoverpolishing process can be at a uniform pressure for all zones of thesubstrate, e.g., 1 to 1.5 psi. The overpolishing process can have apreset duration, e.g., 10 to 15 seconds.

In some implementations, polishing of the substrates does not haltsimultaneously. In such implementations, for the purpose of the endpointdetermination, there can be a reference zone for each substrate. Oncethe index trace of a reference zone of a particular substrate reachesthe target index (e.g., as calculated by the time the linear functionfit the sequence of index values after time T0 reaches the targetindex), endpoint is called for the particular substrate and applicationof pressure to all zones of the particular is halted simultaneously.However, polishing of one or more other substrates can continue. Onlyafter endpoint has been called for the all of the remaining substrates(or after overpolishing has been completed for all substrates), based onthe reference zones of the remaining substrates, does rinsing of thepolishing pad commence. In addition, all of the carrier heads can liftthe substrates off the polishing pad simultaneously.

Where multiple index traces are generated for a particular zone andsubstrate, e.g., one index trace for each library of interest to theparticular zone and substrate, then one of the index traces can beselected for use in the endpoint or pressure control algorithm for theparticular zone and substrate. For example, the each index tracegenerated for the same zone and substrate, the controller 190 can fit alinear function to the index values of that index trace, and determine agoodness of fit of that linear function to the sequence of index values.The index trace generated having the line with the best goodness of fitits own index values can be selected as the index trace for theparticular zone and substrate. For example, when determining how toadjust the polishing rates of the adjustable zones, e.g., at time T0,the linear function with the best goodness of fit can be used in thecalculation. As another example, endpoint can be called when thecalculated index (as calculated from the linear function fit to thesequence of index values) for the line with the best goodness of fitmatches or exceeds the target index. Also, rather than calculating anindex value from the linear function, the index values themselves couldbe compared to the target index to determine the endpoint.

Determining whether an index trace associated with a spectra library hasthe best goodness of fit to the linear function associated with thelibrary can include determining whether the index trace of theassociated spectra library has the least amount of difference from theassociated robust line, relatively, as compared to the differences fromthe associated robust line and index trace associated with anotherlibrary, e.g., the lowest standard deviation, the greatest correlation,or other measure of variance. In one implementation, the goodness of fitis determined by calculating a sum of squared differences between theindex data points and the linear function; the library with the lowestsum of squared differences has the best fit.

In some implementations, the initial thicknesses of two layers on thetwo substrates to be polished on the same platen can be different. Insuch cases, the polish time for the substrates with differentthicknesses can be set or adjusted independently such that the polishingendpoints for the two substrates are substantially the same. Referringto FIG. 12, a plot of index as a function of time to illustrate anexemplary calculation of time offset between the polish start-times oftwo substrates of differing thickness. In this example, the line 405represents an expected index line for a first substrate and the line 410represents an expected index line for a second substrate as thesubstrates are polished to a desired target index IT. The pre-polishindex value for the first substrate and the second substrate(corresponding to thicknesses T1 and T2, respectively) are I_(T1) andI_(T2), respectively, while the target index for both substrates is IT.Even though the example in FIG. 12 shows a same target index for bothsubstrates, in some implementations, each substrate can have a separatetarget index. In such cases, a first target index (or a first targetthickness) and a second target index (or a second target thickness) canbe stored and acted upon by the polishing apparatus. In general, theindex value of a substrate has an inverse relationship with thethickness of the substrate. A higher index value typically correspondsto a smaller thickness. Therefore, in the present example, the thicknessT1 of the first substrate is greater than the thickness T2 of the secondsubstrate.

The thickness T1 and T2 can be measured by taking pre-polishmeasurements, and the corresponding index values can be calculated fromsuch measurements. Measurement can be performed at a metrology systemother than the optical monitoring system to be used during polishing,e.g., an in-line metrology station, such as a profilometer or opticalmetrology station that uses ellipsometry. “In-line” metrology refers tomeasurements made inside the cleanroom or inside a load lock or transferchamber, whereas “in-situ” metrology refers to measurements made insidea process chamber while the processing, e.g., polishing, is actuallyoccurring.

A polishing rate is the rate at which material is removed from asubstrate by polishing and is typically a function of the pressureapplied via the polishing head, platen rotation rate, and slurry flow.Polishing rates (e.g. R1 and R2) can be represented as gradients ofcorresponding index lines. A higher gradient represents a fasterpolishing or removal rate while a smaller gradient represents a slowerremoval rate. For example, in FIG. 12, the polishing rate R1corresponding to the first substrate is higher than the polishing rateR2 corresponding to the second substrate.

Based on the pre-polish thickness (or index value) of the substrate, thetarget index and a knowledge of a polishing rate, an expected requiredpolish time can be calculated. In the example shown in FIG. 12, theexpected required first polish time for polishing the first substratecan be calculated as:

$T_{{est}\; 1} = \frac{{IT} - I_{T\; 1}}{R\; 1}$Similarly, the expected required second polish time for the secondsubstrate in this example can be calculated as:

$T_{{est}\; 2} = \frac{{IT} - I_{T\; 2}}{R\; 2}$If the target index for the two substrates are different, the aboveequations are modified by replacing the value of IT with appropriatetarget index values.

If the expected required polish time for one substrate is higher thanthe other, polishing of the latter substrate is started after a timeoffset with respect to the other substrate such that the expectedpolishing of the two substrates ends substantially simultaneously. Inthe current example, since T_(est2)>T_(est1), the polishing of the firstsubstrate is started after a time period following the start time forthe second substrate. The difference in time between the expectedrequired polish times of the two substrates can be represented as T. Inthe current example, the time period T can be calculated as:T=T _(est2) −T _(est1)

In particular, although the two substrates may be on the same polishingpad simultaneously, for an initial time period T at the beginning of thepolishing operation, no pressure is applied to the substrate having thelesser expected polishing time, while pressure is applied to thesubstrate having the greater expected polishing time. In contrast, afterthe initial time period T, pressure is applied to both substrates.

Referring now to FIG. 13, a plot illustrates an exemplary calculation oftime offset between the polish start-times of two substrates where thepolishing or removal rate R2 corresponding to the thicker (i.e. with agreater pre-polish thickness and lower pre-polish index value) substrateis less than the polishing rate R1 for the thinner (i.e. with a lowerpre-polish thickness and higher pre-polish index value) substrate. Insuch cases, the calculated time offsets are typically large since thethinner substrate erodes relatively quickly to reach the target index.

For the situations in both FIGS. 12 and 13, the lines 405 and 410 arebased on expected polishing rates that are usually known a priori basedon earlier data (i.e., the expected polishing rate for a substrate isnot based on data collected in-situ from that substrate duringpolishing). For example, in some implementations, an expected polishingrate can be the last known polishing rate for a given polishing head. Anexpected polishing rate can also be estimated by calculating an averageor weighted average of multiple last known polishing rates. For example,the expected polishing rate can be determined by calculating a movingaverage of measured polishing rates of a plurality of substratespolished on the polishing pad before polishing of the first substrateand the second substrate.

In some implementations, the expected polishing rates for differentsubstrates can be substantially the same. In such cases, thecorresponding expected index lines are parallel and possibly coincidenton each other if an appropriate delay in polishing is performed. Also,in such cases, the substrate with the thinner layer will be the one towhich no pressure is applied during the initial time period T, whilepressure is applied to the substrate with the thicker layer.

In some situations, the actual polishing rate can deviate from theexpected or projected polishing rates. Therefore, in someimplementations, an adjustment to a polishing parameters of at least onesubstrate can be performed during the polishing, e.g., as describedabove with reference to FIGS. 6-11. For example, the actual polishingrates can be measured, for example, by fitting lines on in situmeasurements of index values. At an intermediate time (i.e. before theestimated end time) T0, the actual polishing rate for the firstsubstrate can be measured by fitting a line 415 on the in situmeasurements 412 of index values. If the actual or measured polishingrate is found to be deviating from the projected polishing rate, interimmodifications can be made to ensure that the substrates reach theirpolishing end point simultaneously. For example, if the polishing ratecorresponding to the first substrate is determined to be less than theprojected polishing rate R1, the pressure on the corresponding polishinghead can be increased such that the polishing rate is represented by thegradient of the line 420 and the entire polishing process for the firstsubstrate is completed in time T_(est1). The pressure adjustment can beapplied a short time after the actual polishing rate is determined.

In some implementations, interim modifications can also be made for thesecond substrate. The actual polishing rate for the second substrate canbe measured, for example at an intermediate time T0′, by fitting a line425 on the in situ measurements 422 of index values. If the slope of theline 425 is found to be different from the slope of the line 410, theactual polishing rate is determined to be deviated from the projectedpolishing rate and pressure adjustments can be done accordingly. In theexample of FIG. 13, the actual polishing rate corresponding to the line425 is more than the projected polishing rate R2. In such a case, thepressure on the polishing head can be reduced such that the entirepolishing process of the second substrate is completed in time T_(est2).In some implementations, the intermediate time points T0 and T0′ can bemade to coincide with each other. In such cases, the interimmeasurements and/or pressure adjustments on different substrates areperformed simultaneously.

In some implementations, the pressure adjustment can also be done foronly one of the substrates, e.g. the first substrate, while allowing theother substrate, e.g., the second substrate, to be polished at thecorresponding actual polishing rate. In such a case, the pressureadjustment for the first substrate is made such that the correspondingendpoint converges on a revised estimated endpoint time calculated basedon the actual polishing rate of the second substrate.

In some implementations, the pressure from the polishing heads areadjusted before the start of the polishing process such that thethickness of the substrates are substantially close to each other at apredetermined time point, e.g., the intermediate time T0 or at anestimated end time. For example, a pressure ratio of the polishing headscan be determined based on the expected required first polish time andthe expected required second polish time. The pressure ratio can bedetermined such that the first substrate and the second substrate havecloser to a same thickness at an estimated end time or an intermediatetime than without such a pressure difference. In some implementationsthe pressure ratio between the polishing heads is substantially equal tothe ratio between the expected required second polish time and theexpected required first polish time and calculated as:

$P_{ratio} = {\frac{P_{2}}{P_{1}} = \frac{T_{{est}\; 2}}{T_{{est}\; 1}}}$wherein P₂ and P₁ are the pressures applied to the heads correspondingto the second and first substrates, respectively. When a pressure ratioapproach is used, the polishing of the two substrates are typicallycommenced together without a time offset T.

In some implementations, a combination of time offset and adjustment ofthe pressure from the carrier heads can be used. For example, a timeoffset T′ can be selected that is greater than zero but less than thetime offset T that would be calculated using the technique describedabove, i.e., 0<T′<T_(est2)−T_(est1). The pressure ratio can be selectedto compensate for the remaining difference, e.g., the pressure ratio canbe calculated as:

$P_{ratio} = {\frac{P_{2}}{P_{1}} = \frac{T_{{est}\; 2} - T^{\prime}}{T_{{est}\; 1}}}$

Referring to FIG. 14, a summary flow chart 600 is illustrated. Aplurality of zones of a plurality of substrates are polished in apolishing apparatus simultaneously with the same polishing pad (step602), as described above. During this polishing operation, each zone ofeach substrate has its polishing rate controllable independently of theother substrates by an independently variable polishing parameter, e.g.,the pressure applied by the chamber in carrier head above the particularzone. During the polishing operation, the substrates are monitored (step604) as described above, e.g., with a measured spectrum obtained fromeach zone of each substrate. The reference spectrum that is the bestmatch is determined (step 606). The index value for each referencespectrum that is the best fit is determined to generate sequence ofindex values (step 610). For each zone of each substrate, a linearfunction is fit to the sequence of index values (step 610). In oneimplementation, an expected endpoint time that the linear function for areference zone will reach a target index value is determined, e.g., bylinear interpolation of the linear function (step 612). In otherimplementations, the expected endpoint time is predetermined orcalculated as a combination of expected endpoint times of multiplezones. If needed, the polishing parameters for the other zones of theother substrates are adjusted to adjust the polishing rate of thatsubstrate such that the plurality of zones of the plurality ofsubstrates reach the target thickness at approximately the same time orsuch that the plurality of zones of the plurality of substrates haveapproximately the same thickness (or a target thickness) at the targettime (step 614). Polishing continues after the parameters are adjusted,and for each zone of each substrate, measuring a spectrum, determiningthe best matching reference spectrum from a library, determining theindex value for the best matching spectrum to generate a new sequence ofindex values for the time period after the polishing parameter has beenadjusted, and fitting a linear function to index values (step 616).Polishing can be halted once the index value for a reference zone (e.g.,a calculated index value generated from the linear function fit to thenew sequence of index values) reaches target index (step 630).

The techniques described above can also be applicable for monitoring ofmetal layers using an eddy current system. In this case, rather thanperforming matching of spectra, the layer thickness (or a valuerepresentative thereof) is measured directly by the eddy currentmonitoring system, and the layer thickness is used in place of the indexvalue for the calculations.

The method used to adjust endpoints can be different based upon the typeof polishing performed. For copper bulk polishing, a single eddy currentmonitoring system can be used. For copper-clearing CMP with multiplewafers on a single platen, a single eddy current monitoring system canfirst be used so that all of the substrates reach a first breakthroughat the same time. The eddy current monitoring system can then beswitched to a laser monitoring system to clear and over-polish thewafers. For barrier and dielectric CMP with multiple wafers on a singleplaten, an optical monitoring system can be used.

Embodiments of the invention and all of the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, or in computer software, firmware, or hardware, including thestructural means disclosed in this specification and structuralequivalents thereof, or in combinations of them. Embodiments of theinvention can be implemented as one or more computer program products,i.e., one or more computer programs tangibly embodied in amachine-readable storage media, for execution by, or to control theoperation of, data processing apparatus, e.g., a programmable processor,a computer, or multiple processors or computers. A computer program(also known as a program, software, software application, or code) canbe written in any form of programming language, including compiled orinterpreted languages, and it can be deployed in any form, including asa stand-alone program or as a module, component, subroutine, or otherunit suitable for use in a computing environment. A computer programdoes not necessarily correspond to a file. A program can be stored in aportion of a file that holds other programs or data, in a single filededicated to the program in question, or in multiple coordinated files(e.g., files that store one or more modules, sub-programs, or portionsof code). A computer program can be deployed to be executed on onecomputer or on multiple computers at one site or distributed acrossmultiple sites and interconnected by a communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

The above described polishing apparatus and methods can be applied in avariety of polishing systems. Either the polishing pad, or the carrierheads, or both can move to provide relative motion between the polishingsurface and the substrate. For example, the platen may orbit rather thanrotate. The polishing pad can be a circular (or some other shape) padsecured to the platen. Some aspects of the endpoint detection system maybe applicable to linear polishing systems, e.g., where the polishing padis a continuous or a reel-to-reel belt that moves linearly. Thepolishing layer can be a standard (for example, polyurethane with orwithout fillers) polishing material, a soft material, or afixed-abrasive material. Terms of relative positioning are used; itshould be understood that the polishing surface and substrate can beheld in a vertical orientation or some other orientation.

Particular embodiments of the invention have been described. Otherembodiments are within the scope of the following claims.

What is claimed is:
 1. A computer-implemented method of polishing, comprising: measuring a first pre-polish thickness of a layer of a first substrate at an in-line metrology station; measuring a second pre-polish thickness of a layer of a second substrate at the in-line metrology station; simultaneously contacting the first substrate and the second substrate to the same polishing pad, wherein pressures applied to the first substrate and the second substrate are independently controllable; determining a difference between a first expected required polish time for the first substrate and a second expected required polish time for the second substrate using the first pre-polish thickness and the second pre-polish thickness; determining a duration of an initial period based on the difference between the first expected required polish time and the second expected required polish time; for the initial period at a beginning of a polishing operation, applying no pressure to whichever of the first substrate and the second substrate has a lesser expected required polish time while simultaneously applying pressure to whichever of the first substrate and the second substrate has a greater expected required polish time; and after the initial period, applying pressure to both the first substrate and the second substrate.
 2. The method of claim 1, further comprising storing a first target thickness for the first substrate and a second target thickness for the second substrate.
 3. The method of claim 2, wherein the duration of the initial period is selected such that a thickness difference between the first substrate and the second substrate is closer to a difference between the first target thickness and the second target thickness at an intermediate time before a projected endpoint time than without such an initial period.
 4. The method of claim 3, wherein the first target thickness is equal to the second target thickness.
 5. The method of claim 4, wherein the first target thickness and the second target thickness are zero.
 6. The method of claim 5, wherein the layer of the first substrate and the layer of the second substrate are metal.
 7. The method of claim 2, further comprising subtracting the first target thickness from the first pre-polish thickness to determine a first amount to remove from the first substrate and subtracting the second target thickness from the second pre-polish thickness to determine a second amount to remove from the second substrate.
 8. The method of claim 7, wherein determining the difference between the first expected required polish time and the second expected required polish time comprises storing a polishing rate calculated prior to polishing of the first substrate and the second substrate.
 9. The method of claim 8, wherein determining the difference between the first expected required polish time and the second expected required polish time comprises dividing the first amount to remove by the polishing rate to determine the first expected required polish time, and dividing the second amount to remove by the polishing rate to determine the second expected required polish time.
 10. The method of claim 8, further comprising calculating the polishing rate by determining the polishing rate of at least one substrate polished on the polishing pad before polishing of the first substrate and the second substrate.
 11. The method of claim 10, wherein determining the polishing rate comprises calculating a moving average of polishing rates of a plurality of substrates polished on the polishing pad before polishing of the first substrate and the second substrate.
 12. The method of claim 1, wherein the initial period equals the difference between the first expected required polish time and the second expected required polish time.
 13. The method of claim 1, further comprising: monitoring the first substrate and the second substrate during polishing with an in-situ monitoring system; at a time after the initial period, adjusting the pressure of at least one of the first or second substrate such that the first substrate and the second substrate reach target thickness at closer to the same time than without such adjustment. 